2 The conceptual basis of the individuality interpretation of quantum theory

According to the assumptions above, an individuality interpretation of a probabilistic theory
does not make sense. This means that the boundaries of this simple framework have to be left
far behind in order to establish QT as a theory about single particles. There are individuality
interpretations which require more than a single universe or the participation of the observer’s
brain [3]. We shall not discuss such interpretations here but restrict ourselves to the standard,
Copenhagen interpretation (CI). In order to overcome the fundamental conflict between
deterministic and probabilistic predictions the CI denies the reality of unobserved
properties [21]. The properties ’come into being’ by the act of measurement in a way which is
unknown and presents an unsolvable ’measurement problem’. The CI ’solves’ the fundamental
conflict in a sophistic sense because it is not the task of a physical theory to make
predictions about non-existing things. But it does not answer the question how things
come back to reality. The CI’s claim for an individuality interpretation may also be
expressed by the statement that QT is a ’complete’ theory as regards the description of
individual particles; a more detailed analysis of the term ’complete’ will be given in
section 4.

The CI shows several strange features, which have as a common origin the switching forth
and back between reality and un-reality of properties as observation begins and ends. This
problem becomes more stringent if two conjugate properties (non-commuting observables) have
to be measured at the same time. A number of principles or concepts have been introduced, by
the founders of the CI, in order to support the individuality interpretation and to explain its
strange features. There seem to be essentially three such principles. Let us begin
with

Heisenberg’s uncertainty principle, the well-known inequality expressing the
impossibility to measure position and momentum of a single particle simultaneously
with arbitrary high precision.

This principle will be referred to as individual uncertainty principle (IUP). The IUP presents the
most important cornerstone of the CI because it supports, if true, the idea that certain
(conjugate) properties of a single microscopic system cannot be simultaneously real. The second
concept supporting the CI is

the particle-wave duality: Depending on the experimental situation individual
microscopic systems may behave either like particles or like waves.

This idea can be considered as a complement to the IUP. In fact, according to the IUP
particles have either sharp values of position or of momentum, depending on the
experimental conditions. The former case corresponds to the particle picture, the latter to
the wave picture. The degree of reality of these two pictures is determined by the
measurement arrangement. The third idea supporting the CI is expressed as an assertion
about

the classical limit of QT: Classical mechanics may be regarded as the limiting case
of quantum mechanics when tends to zero [7]

The relevance of this last point for the individuality interpretation is obvious. If QT really describes
individual particles (for nonzero ), then it should not change its character - as a theory
describing individual particles - if the limit is performed. This limit must agree with a
classical individualistic theory, namely classical mechanics. Otherwise the CI as an individuality
interpretation must be called into doubt.

An important point to note is that no one of these three principles is part of
the quantum theoretical formalism. This means each one needs justification from
experiment or theory. A second important point is that these principles have been set up
in the first half of the last century and that enormous technological progress has
been made since then. A re-examination, taking today’s results into account, seems
useful.